IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Log in (now much improved!) to save this paper

Perturbation methods for Markov-switching DSGE models

  • Foerster, Andrew

    ()

    (Federal Reserve Bank of Atlanta)

  • Rubio-Ramírez, Juan

    ()

    (Duke University)

  • Waggoner, Daniel F.

    ()

    (Federal Reserve Bank of Atlanta)

  • Zha, Tao

    ()

This paper develops a general perturbation methodology for constructing high-order approximations to the solutions of Markov-switching DSGE models. We introduce an important and practical idea of partitioning the Markov-switching parameter space so that a steady state is well defined. With this definition, we show that the problem of finding an approximation of any order can be reduced to solving a system of quadratic equations. We propose using the theory of Grobner bases in searching all the solutions to the quadratic system. This approach allows us to obtain all the approximations and ascertain how many of them are stable. Our methodology is applied to three models to illustrate its feasibility and practicality.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.frbatlanta.org/documents/pubs/wp/wp1301.pdf
Download Restriction: no

Paper provided by Federal Reserve Bank of Atlanta in its series FRB Atlanta Working Paper with number 2013-01.

as
in new window

Length: 84 pages
Date of creation: 01 Mar 2013
Date of revision:
Handle: RePEc:fip:fedawp:2013-01
Contact details of provider: Postal:
1000 Peachtree St., N.E., Atlanta, Georgia 30309

Phone: 404-521-8500
Web page: http://www.frbatlanta.org/
Email:


More information through EDIRC

Order Information: Email:


References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Farmer, Roger E.A. & Waggoner, Daniel F. & Zha, Tao, 2011. "Minimal state variable solutions to Markov-switching rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 35(12), pages 2150-2166.
  2. Troy A. Davig & Eric M. Leeper & Todd B. Walker, 2010. ""Unfunded liabilities" and uncertain fiscal financing," Research Working Paper RWP 10-09, Federal Reserve Bank of Kansas City.
  3. Peralta Alva, Adrián & Santos, Manuel S., 2003. "Accuracy of simulations for stochastic dynamic models," UC3M Working papers. Economics we034615, Universidad Carlos III de Madrid. Departamento de Economía.
  4. Troy A. Davig & Eric M. Leeper, 2005. "Generalizing the Taylor principle," Research Working Paper RWP 05-13, Federal Reserve Bank of Kansas City.
  5. Francesco Bianchi & Leonardo Melosi, 2012. "Modeling the Evolution of Expectations and Uncertainty in General Equilibrium," PIER Working Paper Archive 13-042, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  6. Martin M. Andreasen & Jesús Fernández-Villaverde & Juan Rubio-Ramírez, 2013. "The Pruned State-Space System for Non-Linear DSGE Models: Theory and Empirical Applications," NBER Working Papers 18983, National Bureau of Economic Research, Inc.
  7. Thomas Lubik & Frank Schorfheide, 2002. "Testing for Indeterminacy:An Application to U.S. Monetary Policy," Economics Working Paper Archive 480, The Johns Hopkins University,Department of Economics, revised Jun 2003.
  8. Tauchen, George, 1986. "Finite state markov-chain approximations to univariate and vector autoregressions," Economics Letters, Elsevier, vol. 20(2), pages 177-181.
  9. Eric M. Leeper & Tao Zha, 2002. "Modest policy interventions," FRB Atlanta Working Paper 2002-19, Federal Reserve Bank of Atlanta.
  10. Schmitt-Grohé, Stephanie & Uribe, Martín, 2001. "Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function," CEPR Discussion Papers 2963, C.E.P.R. Discussion Papers.
  11. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, March.
  12. Richard Clarida & Jordi Galí & Mark Gertler, 1997. "Monetary policy rules and macroeconomic stability: Evidence and some theory," Economics Working Papers 350, Department of Economics and Business, Universitat Pompeu Fabra, revised May 1999.
  13. Aldrich, Eric M. & Fernández-Villaverde, Jesús & Ronald Gallant, A. & Rubio-Ramírez, Juan F., 2011. "Tapping the supercomputer under your desk: Solving dynamic equilibrium models with graphics processors," Journal of Economic Dynamics and Control, Elsevier, vol. 35(3), pages 386-393, March.
  14. Fernández-Villaverde, Jesús & Rubio-Ramírez, Juan Francisco, 2006. "Estimating Macroeconomic Models: A Likelihood Approach," CEPR Discussion Papers 5513, C.E.P.R. Discussion Papers.
  15. Frank Smets & Raf Wouters, 2007. "Shocks and Frictions in US Business Cycles : a Bayesian DSGE Approach," Working Paper Research 109, National Bank of Belgium.
  16. Christopher A. Sims & Tao Zha, 2005. "Were There Regime Switches in U.S. Monetary Policy?," Working Papers 92, Princeton University, Department of Economics, Center for Economic Policy Studies..
  17. Frank Schorfheide, 2005. "Learning and Monetary Policy Shifts," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 8(2), pages 392-419, April.
  18. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-84, March.
  19. Jesús Fernández-Villaverde & Pablo Guerrón-Quintana & Juan F. Rubio-Ramírez, 2013. "Estimating dynamic equilibrium models with stochastic volatility," Working Papers 13-19, Federal Reserve Bank of Philadelphia.
  20. Jesus Fernandez-Villaverde & Pablo Guerron-Quintana & Juan F. Rubio-Ramírez & Martin Uribe, 2009. "Risk Matters: The Real Effects of Volatility Shocks," PIER Working Paper Archive 09-013, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  21. Zheng Liu & Daniel F. Waggoner & Tao Zha, 2011. "Sources of macroeconomic fluctuations: A regime‐switching DSGE approach," Quantitative Economics, Econometric Society, vol. 2(2), pages 251-301, 07.
  22. Nicholas Bloom, 2009. "The Impact of Uncertainty Shocks," Econometrica, Econometric Society, vol. 77(3), pages 623-685, 05.
  23. Davig, Troy & Leeper, Eric M. & Walker, Todd B., 2011. "Inflation and the fiscal limit," European Economic Review, Elsevier, vol. 55(1), pages 31-47, January.
  24. Francesco Bianchi, 2013. "Regime Switches, Agents' Beliefs, and Post-World War II U.S. Macroeconomic Dynamics," Review of Economic Studies, Oxford University Press, vol. 80(2), pages 463-490.
  25. Jesus Fernández-Villaverde & Pablo Guerrón-Quintana & Juan F. Rubio-Ramírez, 2010. "Fortune or virtue: time-variant volatilities versus parameter drifting," Working Papers 10-14, Federal Reserve Bank of Philadelphia.
  26. Troy Davig & Taeyoung Doh, 2014. "Monetary Policy Regime Shifts and Inflation Persistence," The Review of Economics and Statistics, MIT Press, vol. 96(5), pages 862-875, December.
  27. Amisano, Gianni & Tristani, Oreste, 2011. "Exact likelihood computation for nonlinear DSGE models with heteroskedastic innovations," Journal of Economic Dynamics and Control, Elsevier, vol. 35(12), pages 2167-2185.
  28. Svensson, Lars E O & Williams, Noah, 2007. "Monetary Policy with Model Uncertainty: Distribution Forecast Targeting," CEPR Discussion Papers 6331, C.E.P.R. Discussion Papers.
  29. Glenn D. Rudebusch & Eric T. Swanson, 2008. "Examining the bond premium puzzle with a DSGE model," Working Paper Series 2007-25, Federal Reserve Bank of San Francisco.
  30. Farmer, Roger E.A. & Waggoner, Daniel F. & Zha, Tao, 2009. "Understanding Markov-switching rational expectations models," Journal of Economic Theory, Elsevier, vol. 144(5), pages 1849-1867, September.
  31. S. Boragan Aruoba & Jesus Fernandez-Villaverde & Juan F. Rubio-Ramirez, 2003. "Comparing Solution Methods for Dynamic Equilibrium Economies," PIER Working Paper Archive 04-003, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  32. Kubler, Felix & Schmedders, Karl, 2010. "Competitive equilibria in semi-algebraic economies," Journal of Economic Theory, Elsevier, vol. 145(1), pages 301-330, January.
  33. Huixin Bi & Nora Traum, 2012. "Estimating Sovereign Default Risk," American Economic Review, American Economic Association, vol. 102(3), pages 161-66, May.
  34. Ruchira Datta, 2010. "Finding all Nash equilibria of a finite game using polynomial algebra," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 55-96, January.
  35. Klein, Paul, 2000. "Using the generalized Schur form to solve a multivariate linear rational expectations model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(10), pages 1405-1423, September.
  36. Lombardo, Giovanni, 2010. "On approximating DSGE models by series expansions," Working Paper Series 1264, European Central Bank.
  37. Paul Gomme & Paul Klein, 2009. "Second-order approximation of dynamic models without the use of tensors," Working Papers 09004, Concordia University, Department of Economics, revised 28 Apr 2010.
  38. Andrew P Blake & Fabrizio Zampolli, 2006. "Optimal monetary policy in Markov-switching models with rational expectations agents," Bank of England working papers 298, Bank of England.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:fip:fedawp:2013-01. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Elaine Clokey)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.